Goldilocks math

Watching CNBC is not something that is done around here very often, but occasionally a few minutes of Power Lunch or Closing Bell will be tuned in just to see how things are going. Similarly, Andy Griffith reruns are favored over Kudlow, Cramer, and Fast Money since, even when skipping all the commercials, it's hard not to come away from these programs without feeling manipulated in one way or another.

Such was the case yesterday on Larry Kudlow's show when the discussion turned to the "near or already here" recession that the show's host has come to grudgingly accept as the reality on the ground.

"Recessions aren't such a bad thing", quipped Larry, "They've happened ten times in the postwar era and look what we have to show for it." A graphic was then shown (recreated below) and guests with opposing viewpoints were prodded to come around to the host's unwavering view that now is a good time to buy stocks.

Now, even with engineering math skills honed over years and years of school and work in private industry, yours truly still sometimes has a hard time with percentage gains, but that 86,677% number just looked freakishly large.

All the other figures seemed to make sense - over a 60 year period you get a lot of compounding, so a 3.4 percent GDP growth coming out to 634% over 60 years sounds reasonable.

In fact, to verify a proper understanding of how percentage gains are calculated you can go to the Wikipedia entry for Percentage and find out more than you ever wanted to know on the subject.

Here, the key passage as it applies to those big 60-year percent gains is:

Although percentages are usually used to express numbers between zero and one, any dimensionless proportionality can be expressed as a percentage. For instance, 111% is 1.11 and −0.35% is −0.0035.

So, the 634% increase in GDP would mean [insert] an incease of [/insert] 6.34 times the GDP in 1947 and the 87,667% gain in the S&P500 would mean [insert] an incease of [/insert] 876.67 times the stock market value at that same time.

That seems pretty simple, but those two numbers - 6.34 and 877 - seem to be way out of whack. Stocks went up at 138 times the rate of real economic growth?

It's easy enough to look up GDP, for example at Measuring Worth you'll find that real GDP in 1947 was $1574.5 billion, which, when multiplied by 6.34 yields $9,982 billion. Add the gain to the original value and you get somewhere close to the $10.1 trillion in the CNBC graphic.

But what about that S&P500 claim, the big number that Larry beat his guests over the head with in a never ending effort to encourage his American viewing audience to keep buying stocks?

What was the value of the S&P500 in 1947? Well, that's a hard question to answer because, according to this source, the S&P500 didn't exist until ten years later.

1957 -- The "416" becomes the Standard & Poor's 500 Composite Stock Price Index. Thanks to technological advancements, computers are introduced and permit the "500" to be calculated and disseminated at one-minute intervals throughout the trading day. In order to create a lengthy historical time series, the new "500" is linked to the 90 Stock Composite Price Index-daily S&P 500 Index prices become available back to 1928. The original "233" and "90" stock indices have evolved into the modern "500". The "500" now consists of 425 Industrials, 60 Utilities and 15 Rails, and has a base period of 1941-43=10.

Oh well, how about using the Dow Jones Industrial Average instead?

Finding the value of the Dow in 1947 is pretty easy - just go to Dow Jones and you can get these really cool charts, one for each decade.
So, it looks like it averaged about 180 during 1947, right around the time of the Marshall Plan and just prior to the invention of the tranisistor (these charts really are very good - I remember splicing them together and hanging them up on a wall sometime in the early 1990s).

So what would the Dow be today after a gain of 87,677% from 1947?

180 + 180 * 876.77 = 158,000

Oops! Now, that's real Goldilocks math!

The percent increase that they were probably going for was 8,767%.

What's an order of magnitude between friends?